Problem: The equation of a circle $C$ is $x^2+y^2-2x+10y-10 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Answer: To find the equation in standard form, complete the square. $(x^2-2x) + (y^2+10y) = 10$ $(x^2-2x+1) + (y^2+10y+25) = 10 + 1 + 25$ $(x-1)^{2} + (y+5)^{2} = 36 = 6^2$ Thus, $(h, k) = (1, -5)$ and $r = 6$.